Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,1,Mod(284,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 6, 5]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.284");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.w (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.521522938201\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{40})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} + x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{20}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
Embedding invariants
Embedding label | 949.1 | ||
Root | \(-0.987688 + 0.156434i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.949 |
Dual form | 1045.1.w.f.664.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(761\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.44168 | + | 1.04744i | −1.44168 | + | 1.04744i | −0.453990 | + | 0.891007i | \(0.650000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(3\) | 0.610425 | + | 1.87869i | 0.610425 | + | 1.87869i | 0.453990 | + | 0.891007i | \(0.350000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(4\) | 0.672288 | − | 2.06909i | 0.672288 | − | 2.06909i | ||||
\(5\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(6\) | −2.84786 | − | 2.06909i | −2.84786 | − | 2.06909i | ||||
\(7\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(8\) | 0.647354 | + | 1.99235i | 0.647354 | + | 1.99235i | ||||
\(9\) | −2.34786 | + | 1.70582i | −2.34786 | + | 1.70582i | ||||
\(10\) | −1.78201 | −1.78201 | ||||||||
\(11\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(12\) | 4.29757 | 4.29757 | ||||||||
\(13\) | 0.734572 | − | 0.533698i | 0.734572 | − | 0.533698i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.610425 | + | 1.87869i | −0.610425 | + | 1.87869i | ||||
\(16\) | −1.26007 | − | 0.915497i | −1.26007 | − | 0.915497i | ||||
\(17\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(18\) | 1.59811 | − | 4.91849i | 1.59811 | − | 4.91849i | ||||
\(19\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(20\) | 1.76007 | − | 1.27877i | 1.76007 | − | 1.27877i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.69480 | − | 0.550672i | −1.69480 | − | 0.550672i | ||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | −3.34786 | + | 2.43236i | −3.34786 | + | 2.43236i | ||||
\(25\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(26\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | ||||
\(27\) | −3.03979 | − | 2.20854i | −3.03979 | − | 2.20854i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(30\) | −1.08779 | − | 3.34786i | −1.08779 | − | 3.34786i | ||||
\(31\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(32\) | 0.680668 | 0.680668 | ||||||||
\(33\) | −1.16110 | + | 1.59811i | −1.16110 | + | 1.59811i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.95106 | + | 6.00473i | 1.95106 | + | 6.00473i | ||||
\(37\) | 0.0966818 | − | 0.297556i | 0.0966818 | − | 0.297556i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(38\) | 1.44168 | + | 1.04744i | 1.44168 | + | 1.04744i | ||||
\(39\) | 1.45106 | + | 1.05425i | 1.45106 | + | 1.05425i | ||||
\(40\) | −0.647354 | + | 1.99235i | −0.647354 | + | 1.99235i | ||||
\(41\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 2.06909 | − | 0.672288i | 2.06909 | − | 0.672288i | ||||
\(45\) | −2.90211 | −2.90211 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(48\) | 0.950759 | − | 2.92614i | 0.950759 | − | 2.92614i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(50\) | −1.44168 | − | 1.04744i | −1.44168 | − | 1.04744i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.610425 | − | 1.87869i | −0.610425 | − | 1.87869i | ||||
\(53\) | 1.14412 | − | 0.831254i | 1.14412 | − | 0.831254i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(54\) | 6.69572 | 6.69572 | ||||||||
\(55\) | 1.00000i | 1.00000i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.59811 | − | 1.16110i | 1.59811 | − | 1.16110i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(60\) | 3.47681 | + | 2.52605i | 3.47681 | + | 2.52605i | ||||
\(61\) | −0.951057 | − | 0.690983i | −0.951057 | − | 0.690983i | − | 1.00000i | \(-0.5\pi\) | |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.278768 | − | 0.202537i | 0.278768 | − | 0.202537i | ||||
\(65\) | 0.907981 | 0.907981 | ||||||||
\(66\) | − | 3.52015i | − | 3.52015i | ||||||
\(67\) | −0.312869 | −0.312869 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(72\) | −4.91849 | − | 3.57349i | −4.91849 | − | 3.57349i | ||||
\(73\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(74\) | 0.172288 | + | 0.530249i | 0.172288 | + | 0.530249i | ||||
\(75\) | −1.59811 | + | 1.16110i | −1.59811 | + | 1.16110i | ||||
\(76\) | −2.17557 | −2.17557 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.19623 | −3.19623 | ||||||||
\(79\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(80\) | −0.481305 | − | 1.48131i | −0.481305 | − | 1.48131i | ||||
\(81\) | 1.39680 | − | 4.29892i | 1.39680 | − | 4.29892i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.23134 | + | 1.69480i | −1.23134 | + | 1.69480i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 4.18391 | − | 3.03979i | 4.18391 | − | 3.03979i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(96\) | 0.415497 | + | 1.27877i | 0.415497 | + | 1.27877i | ||||
\(97\) | 1.44168 | − | 1.04744i | 1.44168 | − | 1.04744i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
0.987688 | − | 0.156434i | \(-0.0500000\pi\) | |||||||
\(98\) | 1.78201 | 1.78201 | ||||||||
\(99\) | −2.76007 | − | 0.896802i | −2.76007 | − | 0.896802i | ||||
\(100\) | 2.17557 | 2.17557 | ||||||||
\(101\) | 1.53884 | − | 1.11803i | 1.53884 | − | 1.11803i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.280582 | + | 0.863541i | −0.280582 | + | 0.863541i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(104\) | 1.53884 | + | 1.11803i | 1.53884 | + | 1.11803i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.778768 | + | 2.39680i | −0.778768 | + | 2.39680i | ||||
\(107\) | −0.0966818 | − | 0.297556i | −0.0966818 | − | 0.297556i | 0.891007 | − | 0.453990i | \(-0.150000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(108\) | −6.61328 | + | 4.80483i | −6.61328 | + | 4.80483i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | −1.04744 | − | 1.44168i | −1.04744 | − | 1.44168i | ||||
\(111\) | 0.618034 | 0.618034 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.280582 | − | 0.863541i | −0.280582 | − | 0.863541i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(114\) | −1.08779 | + | 3.34786i | −1.08779 | + | 3.34786i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.814279 | + | 2.50609i | −0.814279 | + | 2.50609i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.13818 | −4.13818 | ||||||||
\(121\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(122\) | 2.09488 | 2.09488 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.14412 | + | 0.831254i | 1.14412 | + | 0.831254i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(128\) | −0.400087 | + | 1.23134i | −0.400087 | + | 1.23134i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.30902 | + | 0.951057i | −1.30902 | + | 0.951057i | ||||
\(131\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(132\) | 2.52605 | + | 3.47681i | 2.52605 | + | 3.47681i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.451057 | − | 0.327712i | 0.451057 | − | 0.327712i | ||||
\(135\) | −1.16110 | − | 3.57349i | −1.16110 | − | 3.57349i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.863541 | + | 0.280582i | 0.863541 | + | 0.280582i | ||||
\(144\) | 4.52015 | 4.52015 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.610425 | − | 1.87869i | 0.610425 | − | 1.87869i | ||||
\(148\) | −0.550672 | − | 0.400087i | −0.550672 | − | 0.400087i | ||||
\(149\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(150\) | 1.08779 | − | 3.34786i | 1.08779 | − | 3.34786i | ||||
\(151\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(152\) | 1.69480 | − | 1.23134i | 1.69480 | − | 1.23134i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.15688 | − | 2.29360i | 3.15688 | − | 2.29360i | ||||
\(157\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.26007 | + | 1.64204i | 2.26007 | + | 1.64204i | ||||
\(160\) | 0.550672 | + | 0.400087i | 0.550672 | + | 0.400087i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.48912 | + | 7.66072i | 2.48912 | + | 7.66072i | ||||
\(163\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.87869 | + | 0.610425i | −1.87869 | + | 0.610425i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.59811 | + | 1.16110i | −1.59811 | + | 1.16110i | −0.707107 | + | 0.707107i | \(0.750000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.0542543 | + | 0.166977i | −0.0542543 | + | 0.166977i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.34786 | + | 1.70582i | 2.34786 | + | 1.70582i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.437016 | + | 1.34500i | 0.437016 | + | 1.34500i | 0.891007 | + | 0.453990i | \(0.150000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.55754i | − | 1.55754i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(180\) | −1.95106 | + | 6.00473i | −1.95106 | + | 6.00473i | ||||
\(181\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.717598 | − | 2.20854i | 0.717598 | − | 2.20854i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.253116 | − | 0.183900i | 0.253116 | − | 0.183900i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.550672 | + | 1.69480i | 0.550672 | + | 1.69480i | ||||
\(191\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(192\) | 0.550672 | + | 0.400087i | 0.550672 | + | 0.400087i | ||||
\(193\) | −1.59811 | − | 1.16110i | −1.59811 | − | 1.16110i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
−0.707107 | − | 0.707107i | \(-0.750000\pi\) | |||||||
\(194\) | −0.981305 | + | 3.02015i | −0.981305 | + | 3.02015i | ||||
\(195\) | 0.554254 | + | 1.70582i | 0.554254 | + | 1.70582i | ||||
\(196\) | −1.76007 | + | 1.27877i | −1.76007 | + | 1.27877i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 4.91849 | − | 1.59811i | 4.91849 | − | 1.59811i | ||||
\(199\) | 1.61803 | 1.61803 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(200\) | −1.69480 | + | 1.23134i | −1.69480 | + | 1.23134i | ||||
\(201\) | −0.190983 | − | 0.587785i | −0.190983 | − | 0.587785i | ||||
\(202\) | −1.04744 | + | 3.22369i | −1.04744 | + | 3.22369i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.41421 | −1.41421 | ||||||||
\(209\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(212\) | −0.950759 | − | 2.92614i | −0.950759 | − | 2.92614i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.451057 | + | 0.327712i | 0.451057 | + | 0.327712i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.43236 | − | 7.48604i | 2.43236 | − | 7.48604i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.06909 | + | 0.672288i | 2.06909 | + | 0.672288i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.891007 | + | 0.647354i | −0.891007 | + | 0.647354i | ||||
\(223\) | −0.437016 | − | 1.34500i | −0.437016 | − | 1.34500i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
0.453990 | − | 0.891007i | \(-0.350000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.34786 | − | 1.70582i | −2.34786 | − | 1.70582i | ||||
\(226\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | ||||
\(227\) | −0.610425 | + | 1.87869i | −0.610425 | + | 1.87869i | −0.156434 | + | 0.987688i | \(0.550000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(228\) | −1.32802 | − | 4.08723i | −1.32802 | − | 4.08723i | ||||
\(229\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(234\) | −1.45106 | − | 4.46589i | −1.45106 | − | 4.46589i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | 1.00000 | \(0\) | ||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(240\) | 2.48912 | − | 1.80845i | 2.48912 | − | 1.80845i | ||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −0.550672 | − | 1.69480i | −0.550672 | − | 1.69480i | ||||
\(243\) | 5.17160 | 5.17160 | ||||||||
\(244\) | −2.06909 | + | 1.50328i | −2.06909 | + | 1.50328i | ||||
\(245\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.734572 | − | 0.533698i | −0.734572 | − | 0.533698i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.550672 | − | 1.69480i | −0.550672 | − | 1.69480i | ||||
\(251\) | −1.30902 | + | 0.951057i | −1.30902 | + | 0.951057i | −0.309017 | + | 0.951057i | \(0.600000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.52015 | −2.52015 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.606480 | − | 1.86655i | −0.606480 | − | 1.86655i | ||||
\(257\) | 0.280582 | − | 0.863541i | 0.280582 | − | 0.863541i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.987688 | − | 0.156434i | \(-0.0500000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.610425 | − | 1.87869i | 0.610425 | − | 1.87869i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.33269 | − | 1.69480i | 2.33269 | − | 1.69480i | ||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | −3.93564 | − | 1.27877i | −3.93564 | − | 1.27877i | ||||
\(265\) | 1.41421 | 1.41421 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.210338 | + | 0.647354i | −0.210338 | + | 0.647354i | ||||
\(269\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(270\) | 5.41695 | + | 3.93564i | 5.41695 | + | 3.93564i | ||||
\(271\) | −0.587785 | + | 1.80902i | −0.587785 | + | 1.80902i | 1.00000i | \(0.5\pi\) | ||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.97538 | 1.97538 | ||||||||
\(286\) | −1.53884 | + | 0.500000i | −1.53884 | + | 0.500000i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.59811 | + | 1.16110i | −1.59811 | + | 1.16110i | ||||
\(289\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.84786 | + | 2.06909i | 2.84786 | + | 2.06909i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.550672 | + | 1.69480i | −0.550672 | + | 1.69480i | 0.156434 | + | 0.987688i | \(0.450000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(294\) | 1.08779 | + | 3.34786i | 1.08779 | + | 3.34786i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.655423 | 0.655423 | ||||||||
\(297\) | − | 3.75739i | − | 3.75739i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.32802 | + | 4.08723i | 1.32802 | + | 4.08723i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.03979 | + | 2.20854i | 3.03979 | + | 2.20854i | ||||
\(304\) | −0.481305 | + | 1.48131i | −0.481305 | + | 1.48131i | ||||
\(305\) | −0.363271 | − | 1.11803i | −0.363271 | − | 1.11803i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.79360 | −1.79360 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.587785 | − | 1.80902i | −0.587785 | − | 1.80902i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(312\) | −1.16110 | + | 3.57349i | −1.16110 | + | 3.57349i | ||||
\(313\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.14412 | + | 0.831254i | −1.14412 | + | 0.831254i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(318\) | −4.97824 | −4.97824 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.344577 | 0.344577 | ||||||||
\(321\) | 0.500000 | − | 0.363271i | 0.500000 | − | 0.363271i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −7.95579 | − | 5.78022i | −7.95579 | − | 5.78022i | ||||
\(325\) | 0.734572 | + | 0.533698i | 0.734572 | + | 0.533698i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.06909 | − | 2.84786i | 2.06909 | − | 2.84786i | ||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.280582 | + | 0.863541i | 0.280582 | + | 0.863541i | ||||
\(334\) | 1.08779 | − | 3.34786i | 1.08779 | − | 3.34786i | ||||
\(335\) | −0.253116 | − | 0.183900i | −0.253116 | − | 0.183900i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.437016 | − | 1.34500i | 0.437016 | − | 1.34500i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(338\) | −0.0966818 | − | 0.297556i | −0.0966818 | − | 0.297556i | ||||
\(339\) | 1.45106 | − | 1.05425i | 1.45106 | − | 1.05425i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −5.17160 | −5.17160 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.03884 | − | 1.48131i | −2.03884 | − | 1.48131i | ||||
\(347\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.190983 | − | 0.587785i | −0.190983 | − | 0.587785i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.41164 | −3.41164 | ||||||||
\(352\) | 0.400087 | + | 0.550672i | 0.400087 | + | 0.550672i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.363271 | − | 1.11803i | 0.363271 | − | 1.11803i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(360\) | −1.87869 | − | 5.78203i | −1.87869 | − | 5.78203i | ||||
\(361\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.97538 | −1.97538 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.27877 | + | 3.93564i | 1.27877 | + | 3.93564i | ||||
\(367\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.172288 | + | 0.530249i | −0.172288 | + | 0.530249i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.312869 | 0.312869 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.97538 | −1.97538 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(380\) | −1.76007 | − | 1.27877i | −1.76007 | − | 1.27877i | ||||
\(381\) | −0.863271 | + | 2.65688i | −0.863271 | + | 2.65688i | ||||
\(382\) | −0.340334 | − | 1.04744i | −0.340334 | − | 1.04744i | ||||
\(383\) | −1.14412 | + | 0.831254i | −1.14412 | + | 0.831254i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(384\) | −2.55754 | −2.55754 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.52015 | 3.52015 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.19803 | − | 3.68715i | −1.19803 | − | 3.68715i | ||||
\(389\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
1.00000 | \(0\) | |||||||||
\(390\) | −2.58580 | − | 1.87869i | −2.58580 | − | 1.87869i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.647354 | − | 1.99235i | 0.647354 | − | 1.99235i | ||||
\(393\) | −0.987688 | − | 3.03979i | −0.987688 | − | 3.03979i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.71113 | + | 5.10793i | −3.71113 | + | 5.10793i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | −2.33269 | + | 1.69480i | −2.33269 | + | 1.69480i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.481305 | − | 1.48131i | 0.481305 | − | 1.48131i | ||||
\(401\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(402\) | 0.891007 | + | 0.647354i | 0.891007 | + | 0.647354i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1.27877 | − | 3.93564i | −1.27877 | − | 3.93564i | ||||
\(405\) | 3.65688 | − | 2.65688i | 3.65688 | − | 2.65688i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.297556 | − | 0.0966818i | 0.297556 | − | 0.0966818i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.59811 | + | 1.16110i | 1.59811 | + | 1.16110i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.500000 | − | 0.363271i | 0.500000 | − | 0.363271i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.78201i | 1.78201i | ||||||||
\(419\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.39680 | + | 1.74138i | 2.39680 | + | 1.74138i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.680668 | −0.680668 | ||||||||
\(429\) | 1.79360i | 1.79360i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(432\) | 1.80845 | + | 5.56584i | 1.80845 | + | 5.56584i | ||||
\(433\) | 0.550672 | − | 1.69480i | 0.550672 | − | 1.69480i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(440\) | −1.99235 | + | 0.647354i | −1.99235 | + | 0.647354i | ||||
\(441\) | 2.90211 | 2.90211 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(444\) | 0.415497 | − | 1.27877i | 0.415497 | − | 1.27877i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.03884 | + | 1.48131i | 2.03884 | + | 1.48131i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(450\) | 5.17160 | 5.17160 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −1.97538 | −1.97538 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.08779 | − | 3.34786i | −1.08779 | − | 3.34786i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.34786 | + | 2.43236i | 3.34786 | + | 2.43236i | ||||
\(457\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(468\) | 4.63791 | + | 3.36964i | 4.63791 | + | 3.36964i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.26827 | + | 3.90333i | −1.26827 | + | 3.90333i | ||||
\(478\) | −0.891007 | − | 0.647354i | −0.891007 | − | 0.647354i | ||||
\(479\) | −1.53884 | − | 1.11803i | −1.53884 | − | 1.11803i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.587785 | − | 0.809017i | \(-0.700000\pi\) | |||||||
\(480\) | −0.415497 | + | 1.27877i | −0.415497 | + | 1.27877i | ||||
\(481\) | −0.0877853 | − | 0.270175i | −0.0877853 | − | 0.270175i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.76007 | + | 1.27877i | 1.76007 | + | 1.27877i | ||||
\(485\) | 1.78201 | 1.78201 | ||||||||
\(486\) | −7.45579 | + | 5.41695i | −7.45579 | + | 5.41695i | ||||
\(487\) | 0.437016 | + | 1.34500i | 0.437016 | + | 1.34500i | 0.891007 | + | 0.453990i | \(0.150000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(488\) | 0.761010 | − | 2.34215i | 0.761010 | − | 2.34215i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.44168 | + | 1.04744i | 1.44168 | + | 1.04744i | ||||
\(491\) | 0.500000 | − | 1.53884i | 0.500000 | − | 1.53884i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 1.61803 | 1.61803 | ||||||||
\(495\) | −1.70582 | − | 2.34786i | −1.70582 | − | 2.34786i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(500\) | 1.76007 | + | 1.27877i | 1.76007 | + | 1.27877i | ||||
\(501\) | −3.15688 | − | 2.29360i | −3.15688 | − | 2.29360i | ||||
\(502\) | 0.891007 | − | 2.74224i | 0.891007 | − | 2.74224i | ||||
\(503\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.90211 | 1.90211 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.346818 | −0.346818 | ||||||||
\(508\) | 2.48912 | − | 1.80845i | 2.48912 | − | 1.80845i | ||||
\(509\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.78201 | + | 1.29471i | 1.78201 | + | 1.29471i | ||||
\(513\) | −1.16110 | + | 3.57349i | −1.16110 | + | 3.57349i | ||||
\(514\) | 0.500000 | + | 1.53884i | 0.500000 | + | 1.53884i | ||||
\(515\) | −0.734572 | + | 0.533698i | −0.734572 | + | 0.533698i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.26007 | + | 1.64204i | −2.26007 | + | 1.64204i | ||||
\(520\) | 0.587785 | + | 1.80902i | 0.587785 | + | 1.80902i | ||||
\(521\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.734572 | − | 0.533698i | −0.734572 | − | 0.533698i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(524\) | −1.08779 | + | 3.34786i | −1.08779 | + | 3.34786i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2.92614 | − | 0.950759i | 2.92614 | − | 0.950759i | ||||
\(529\) | 1.00000 | 1.00000 | ||||||||
\(530\) | −2.03884 | + | 1.48131i | −2.03884 | + | 1.48131i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0966818 | − | 0.297556i | 0.0966818 | − | 0.297556i | ||||
\(536\) | −0.202537 | − | 0.623345i | −0.202537 | − | 0.623345i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.00000i | − | 1.00000i | ||||||
\(540\) | −8.17447 | −8.17447 | ||||||||
\(541\) | 0.951057 | − | 0.690983i | 0.951057 | − | 0.690983i | − | 1.00000i | \(-0.5\pi\) | |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(542\) | −1.04744 | − | 3.22369i | −1.04744 | − | 3.22369i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.610425 | + | 1.87869i | 0.610425 | + | 1.87869i | 0.453990 | + | 0.891007i | \(0.350000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.41164 | 3.41164 | ||||||||
\(550\) | − | 1.78201i | − | 1.78201i | ||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.44168 | − | 1.04744i | 1.44168 | − | 1.04744i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
0.987688 | − | 0.156434i | \(-0.0500000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.280582 | − | 0.863541i | 0.280582 | − | 0.863541i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(570\) | −2.84786 | + | 2.06909i | −2.84786 | + | 2.06909i | ||||
\(571\) | 1.90211 | 1.90211 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(572\) | 1.16110 | − | 1.59811i | 1.16110 | − | 1.59811i | ||||
\(573\) | −1.22085 | −1.22085 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(577\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(578\) | −1.44168 | − | 1.04744i | −1.44168 | − | 1.04744i | ||||
\(579\) | 1.20582 | − | 3.71113i | 1.20582 | − | 3.71113i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.27295 | −6.27295 | ||||||||
\(583\) | 1.34500 | + | 0.437016i | 1.34500 | + | 0.437016i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.13181 | + | 1.54885i | −2.13181 | + | 1.54885i | ||||
\(586\) | −0.981305 | − | 3.02015i | −0.981305 | − | 3.02015i | ||||
\(587\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(588\) | −3.47681 | − | 2.52605i | −3.47681 | − | 2.52605i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.394238 | + | 0.286431i | −0.394238 | + | 0.286431i | ||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 3.93564 | + | 5.41695i | 3.93564 | + | 5.41695i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.987688 | + | 3.03979i | 0.987688 | + | 3.03979i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(600\) | −3.34786 | − | 2.43236i | −3.34786 | − | 2.43236i | ||||
\(601\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.734572 | − | 0.533698i | 0.734572 | − | 0.533698i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(606\) | −6.69572 | −6.69572 | ||||||||
\(607\) | 1.59811 | − | 1.16110i | 1.59811 | − | 1.16110i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(608\) | −0.210338 | − | 0.647354i | −0.210338 | − | 0.647354i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.69480 | + | 1.23134i | 1.69480 | + | 1.23134i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(614\) | −2.03884 | + | 1.48131i | −2.03884 | + | 1.48131i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 2.58580 | − | 1.87869i | 2.58580 | − | 1.87869i | ||||
\(619\) | −0.363271 | − | 1.11803i | −0.363271 | − | 1.11803i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.74224 | + | 1.99235i | 2.74224 | + | 1.99235i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.863271 | − | 2.65688i | −0.863271 | − | 2.65688i | ||||
\(625\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.87869 | + | 0.610425i | 1.87869 | + | 0.610425i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.587785 | + | 1.80902i | −0.587785 | + | 1.80902i | 1.00000i | \(0.5\pi\) | ||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.778768 | − | 2.39680i | 0.778768 | − | 2.39680i | ||||
\(635\) | 0.437016 | + | 1.34500i | 0.437016 | + | 1.34500i | ||||
\(636\) | 4.91695 | − | 3.57237i | 4.91695 | − | 3.57237i | ||||
\(637\) | −0.907981 | −0.907981 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.04744 | + | 0.761010i | −1.04744 | + | 0.761010i | ||||
\(641\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(642\) | −0.340334 | + | 1.04744i | −0.340334 | + | 1.04744i | ||||
\(643\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(648\) | 9.46917 | 9.46917 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.61803 | −1.61803 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 4.29757i | 4.29757i | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 1.32802 | + | 4.08723i | 1.32802 | + | 4.08723i | ||||
\(669\) | 2.26007 | − | 1.64204i | 2.26007 | − | 1.64204i | ||||
\(670\) | 0.557537 | 0.557537 | ||||||||
\(671\) | − | 1.17557i | − | 1.17557i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.253116 | − | 0.183900i | 0.253116 | − | 0.183900i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(674\) | 0.778768 | + | 2.39680i | 0.778768 | + | 2.39680i | ||||
\(675\) | 1.16110 | − | 3.57349i | 1.16110 | − | 3.57349i | ||||
\(676\) | 0.309017 | + | 0.224514i | 0.309017 | + | 0.224514i | ||||
\(677\) | −1.59811 | − | 1.16110i | −1.59811 | − | 1.16110i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
−0.707107 | − | 0.707107i | \(-0.750000\pi\) | |||||||
\(678\) | −0.987688 | + | 3.03979i | −0.987688 | + | 3.03979i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.90211 | −3.90211 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.78201 | −1.78201 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(684\) | 5.10793 | − | 3.71113i | 5.10793 | − | 3.71113i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.396802 | − | 1.22123i | 0.396802 | − | 1.22123i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.53884 | − | 1.11803i | 1.53884 | − | 1.11803i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(692\) | 3.07672 | 3.07672 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0.891007 | + | 0.647354i | 0.891007 | + | 0.647354i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.587785 | + | 1.80902i | 0.587785 | + | 1.80902i | 0.587785 | + | 0.809017i | \(0.300000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 4.91849 | − | 3.57349i | 4.91849 | − | 3.57349i | ||||
\(703\) | −0.312869 | −0.312869 | ||||||||
\(704\) | 0.327712 | + | 0.106480i | 0.327712 | + | 0.106480i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.533698 | + | 0.734572i | 0.533698 | + | 0.734572i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.987688 | + | 0.717598i | −0.987688 | + | 0.717598i | ||||
\(718\) | 0.647354 | + | 1.99235i | 0.647354 | + | 1.99235i | ||||
\(719\) | 0.363271 | − | 1.11803i | 0.363271 | − | 1.11803i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(720\) | 3.65688 | + | 2.65688i | 3.65688 | + | 2.65688i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.550672 | − | 1.69480i | 0.550672 | − | 1.69480i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.84786 | − | 2.06909i | 2.84786 | − | 2.06909i | ||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.76007 | + | 5.41695i | 1.76007 | + | 5.41695i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −4.08723 | − | 2.96955i | −4.08723 | − | 2.96955i | ||||
\(733\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.59811 | − | 1.16110i | 1.59811 | − | 1.16110i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.183900 | − | 0.253116i | −0.183900 | − | 0.253116i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.30902 | + | 0.951057i | −1.30902 | + | 0.951057i | −0.309017 | + | 0.951057i | \(0.600000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(740\) | −0.210338 | − | 0.647354i | −0.210338 | − | 0.647354i | ||||
\(741\) | 0.554254 | − | 1.70582i | 0.554254 | − | 1.70582i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.44168 | + | 1.04744i | 1.44168 | + | 1.04744i | 0.987688 | + | 0.156434i | \(0.0500000\pi\) |
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.451057 | + | 0.327712i | −0.451057 | + | 0.327712i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.84786 | − | 2.06909i | 2.84786 | − | 2.06909i | ||||
\(751\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.58580 | − | 1.87869i | −2.58580 | − | 1.87869i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.09488 | 2.09488 | ||||||||
\(761\) | −0.951057 | + | 0.690983i | −0.951057 | + | 0.690983i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(762\) | −1.53836 | − | 4.73459i | −1.53836 | − | 4.73459i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.08779 | + | 0.790322i | 1.08779 | + | 0.790322i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.778768 | − | 2.39680i | 0.778768 | − | 2.39680i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 3.13647 | − | 2.27878i | 3.13647 | − | 2.27878i | ||||
\(769\) | −1.17557 | −1.17557 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.79360 | 1.79360 | ||||||||
\(772\) | −3.47681 | + | 2.52605i | −3.47681 | + | 2.52605i | ||||
\(773\) | −0.610425 | − | 1.87869i | −0.610425 | − | 1.87869i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
−0.156434 | − | 0.987688i | \(-0.550000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.02015 | + | 2.19427i | 3.02015 | + | 2.19427i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.340334 | + | 1.04744i | 0.340334 | + | 1.04744i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 3.90211 | 3.90211 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.481305 | + | 1.48131i | 0.481305 | + | 1.48131i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.60793 | + | 3.34786i | 4.60793 | + | 3.34786i | ||||
\(787\) | −0.253116 | − | 0.183900i | −0.253116 | − | 0.183900i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 6.07958i | − | 6.07958i | ||||||
\(793\) | −1.06740 | −1.06740 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.863271 | + | 2.65688i | 0.863271 | + | 2.65688i | ||||
\(796\) | 1.08779 | − | 3.34786i | 1.08779 | − | 3.34786i | ||||
\(797\) | 1.44168 | + | 1.04744i | 1.44168 | + | 1.04744i | 0.987688 | + | 0.156434i | \(0.0500000\pi\) |
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.210338 | + | 0.647354i | 0.210338 | + | 0.647354i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.34458 | −1.34458 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.22369 | + | 2.34215i | 3.22369 | + | 2.34215i | ||||
\(809\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(810\) | −2.48912 | + | 7.66072i | −2.48912 | + | 7.66072i | ||||
\(811\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.75739 | −3.75739 | ||||||||
\(814\) | −0.327712 | + | 0.451057i | −0.327712 | + | 0.451057i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(824\) | −1.90211 | −1.90211 | ||||||||
\(825\) | −1.87869 | − | 0.610425i | −1.87869 | − | 0.610425i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.14412 | − | 0.831254i | 1.14412 | − | 0.831254i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.0966818 | − | 0.297556i | 0.0966818 | − | 0.297556i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.97538 | −1.97538 | ||||||||
\(836\) | −1.27877 | − | 1.76007i | −1.27877 | − | 1.76007i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.891007 | + | 0.647354i | −0.891007 | + | 0.647354i | ||||
\(839\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.142040 | + | 0.103198i | −0.142040 | + | 0.103198i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.20269 | −2.20269 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.896802 | + | 2.76007i | 0.896802 | + | 2.76007i | ||||
\(856\) | 0.530249 | − | 0.385248i | 0.530249 | − | 0.385248i | ||||
\(857\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(858\) | −1.87869 | − | 2.58580i | −1.87869 | − | 2.58580i | ||||
\(859\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.734572 | − | 0.533698i | −0.734572 | − | 0.533698i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(864\) | −2.06909 | − | 1.50328i | −2.06909 | − | 1.50328i | ||||
\(865\) | −0.437016 | + | 1.34500i | −0.437016 | + | 1.34500i | ||||
\(866\) | 0.981305 | + | 3.02015i | 0.981305 | + | 3.02015i | ||||
\(867\) | −1.59811 | + | 1.16110i | −1.59811 | + | 1.16110i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.229825 | + | 0.166977i | −0.229825 | + | 0.166977i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.59811 | + | 4.91849i | −1.59811 | + | 4.91849i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.280582 | + | 0.863541i | 0.280582 | + | 0.863541i | 0.987688 | + | 0.156434i | \(0.0500000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.52015 | −3.52015 | ||||||||
\(880\) | 0.915497 | − | 1.26007i | 0.915497 | − | 1.26007i | ||||
\(881\) | 1.17557 | 1.17557 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(882\) | −4.18391 | + | 3.03979i | −4.18391 | + | 3.03979i | ||||
\(883\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.280582 | + | 0.863541i | −0.280582 | + | 0.863541i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(888\) | 0.400087 | + | 1.23134i | 0.400087 | + | 1.23134i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.29892 | − | 1.39680i | 4.29892 | − | 1.39680i | ||||
\(892\) | −3.07672 | −3.07672 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −5.10793 | + | 3.71113i | −5.10793 | + | 3.71113i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.53884 | − | 1.11803i | 1.53884 | − | 1.11803i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.14412 | − | 0.831254i | −1.14412 | − | 0.831254i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(908\) | 3.47681 | + | 2.52605i | 3.47681 | + | 2.52605i | ||||
\(909\) | −1.70582 | + | 5.24997i | −1.70582 | + | 5.24997i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(912\) | −3.07672 | −3.07672 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.87869 | − | 1.36495i | 1.87869 | − | 1.36495i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.863271 | + | 2.65688i | 0.863271 | + | 2.65688i | ||||
\(922\) | −0.891007 | + | 0.647354i | −0.891007 | + | 0.647354i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.312869 | 0.312869 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.814279 | − | 2.50609i | −0.814279 | − | 2.50609i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.03979 | − | 2.20854i | 3.03979 | − | 2.20854i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.52015 | −5.52015 | ||||||||
\(937\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −0.550672 | + | 1.69480i | −0.550672 | + | 1.69480i | ||||
\(951\) | −2.26007 | − | 1.64204i | −2.26007 | − | 1.64204i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.610425 | − | 1.87869i | 0.610425 | − | 1.87869i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
0.453990 | − | 0.891007i | \(-0.350000\pi\) | |||||||
\(954\) | −2.26007 | − | 6.95579i | −2.26007 | − | 6.95579i | ||||
\(955\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | ||||
\(956\) | 1.34458 | 1.34458 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.38959 | 3.38959 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.210338 | + | 0.647354i | 0.210338 | + | 0.647354i | ||||
\(961\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(962\) | 0.409551 | + | 0.297556i | 0.409551 | + | 0.297556i | ||||
\(963\) | 0.734572 | + | 0.533698i | 0.734572 | + | 0.533698i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.610425 | − | 1.87869i | −0.610425 | − | 1.87869i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | −2.09488 | −2.09488 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.56909 | + | 1.86655i | −2.56909 | + | 1.86655i | ||||
\(971\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(972\) | 3.47681 | − | 10.7005i | 3.47681 | − | 10.7005i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.03884 | − | 1.48131i | −2.03884 | − | 1.48131i | ||||
\(975\) | −0.554254 | + | 1.70582i | −0.554254 | + | 1.70582i | ||||
\(976\) | 0.565808 | + | 1.74138i | 0.565808 | + | 1.74138i | ||||
\(977\) | −1.44168 | + | 1.04744i | −1.44168 | + | 1.04744i | −0.453990 | + | 0.891007i | \(0.650000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.17557 | −2.17557 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.891007 | + | 2.74224i | 0.891007 | + | 2.74224i | ||||
\(983\) | −0.0966818 | + | 0.297556i | −0.0966818 | + | 0.297556i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.59811 | + | 1.16110i | −1.59811 | + | 1.16110i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 4.91849 | + | 1.59811i | 4.91849 | + | 1.59811i | ||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.951057 | + | 0.690983i | −0.951057 | + | 0.690983i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1045.1.w.f.949.1 | yes | 16 | |
5.4 | even | 2 | inner | 1045.1.w.f.949.4 | yes | 16 | |
11.4 | even | 5 | inner | 1045.1.w.f.664.1 | ✓ | 16 | |
19.18 | odd | 2 | inner | 1045.1.w.f.949.4 | yes | 16 | |
55.4 | even | 10 | inner | 1045.1.w.f.664.4 | yes | 16 | |
95.94 | odd | 2 | CM | 1045.1.w.f.949.1 | yes | 16 | |
209.37 | odd | 10 | inner | 1045.1.w.f.664.4 | yes | 16 | |
1045.664 | odd | 10 | inner | 1045.1.w.f.664.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.1.w.f.664.1 | ✓ | 16 | 11.4 | even | 5 | inner | |
1045.1.w.f.664.1 | ✓ | 16 | 1045.664 | odd | 10 | inner | |
1045.1.w.f.664.4 | yes | 16 | 55.4 | even | 10 | inner | |
1045.1.w.f.664.4 | yes | 16 | 209.37 | odd | 10 | inner | |
1045.1.w.f.949.1 | yes | 16 | 1.1 | even | 1 | trivial | |
1045.1.w.f.949.1 | yes | 16 | 95.94 | odd | 2 | CM | |
1045.1.w.f.949.4 | yes | 16 | 5.4 | even | 2 | inner | |
1045.1.w.f.949.4 | yes | 16 | 19.18 | odd | 2 | inner |